Theme engines are responsible for doing the actual output via template files. Although previous versions of Drupal were capable of using different theme engines, one stood out and was used 99.9 percent of the time (statistic made up by me on the spot)--PHPTemplate. This theme engine used PHP files with .tpl.php extension and contained both markup and PHP. Seasoned Drupal developers grew accustomed to this practice, but it was always more difficult for frontend developers to use and theme against.
In Drupal 8, it was abandoned in favor of the Twig templating engine created by SensioLabs (the people responsible for the Symfony project). As mentioned, theme functions were also deprecated in favor of outputting everything through a Twig file. This brought about many improvements to the theme system and quite some joy to the frontend community. For example, it improved security...
